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Varifold-Based Matching of Curves via Sobolev-Type Riemannian Metrics

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Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics (GRAIL 2017, MICGen 2017, MFCA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10551))

Abstract

Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, apply it to study the shape of mosquito wings and compare our method to curve matching in the LDDMM framework.

M. Bauer, M. Bruveris, N. Charon, J. Møller-Andersen—All authors contributed equally to the article.

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Notes

  1. 1.

    We used the publicly available Matlab implementation, which can be downloaded at http://ssamg.stat.fsu.edu/software.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, USA

    Martin Bauer & Jakob Møller-Andersen

  2. Department of Mathematics, Brunel University London, London, England

    Martins Bruveris

  3. CIS, Johns Hopkins University, Baltimore, USA

    Nicolas Charon

Authors
  1. Martin Bauer
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  2. Martins Bruveris
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  3. Nicolas Charon
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  4. Jakob Møller-Andersen
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Corresponding author

Correspondence to Jakob Møller-Andersen .

Editor information

Editors and Affiliations

  1. University College London, London, United Kingdom

    M. Jorge Cardoso

  2. McGill University, Montreal, Québec, Canada

    Tal Arbel

  3. Imperial College London, London, United Kingdom

    Enzo Ferrante

  4. Inria Sophia, Sophia-Antipolis, France

    Xavier Pennec

  5. Harvard Medical School, Massachusetts Institute of Technology, Boston, Massachusetts, USA

    Adrian V. Dalca

  6. Imperial College London, London, United Kingdom

    Sarah Parisot

  7. University of Utah, Salt Lake City, Utah, USA

    Sarang Joshi

  8. University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Nematollah K. Batmanghelich

  9. University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Aristeidis Sotiras

  10. University of Copenhagen, Copenhagen, Denmark

    Mads Nielsen

  11. Cornell University, Ithaca, New York, USA

    Mert R. Sabuncu

  12. University of Utah, Salt Lake City, USA

    Tom Fletcher

  13. University of Indiana, Indianapolis, Indiana, USA

    Li Shen

  14. Brain and Spine Institute, Inria, Paris, France

    Stanley Durrleman

  15. University of Copenhagen, Copenhagen, Denmark

    Stefan Sommer

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Bauer, M., Bruveris, M., Charon, N., Møller-Andersen, J. (2017). Varifold-Based Matching of Curves via Sobolev-Type Riemannian Metrics. In: Cardoso, M., et al. Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics. GRAIL MICGen MFCA 2017 2017 2017. Lecture Notes in Computer Science(), vol 10551. Springer, Cham. https://doi.org/10.1007/978-3-319-67675-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-67675-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67674-6

  • Online ISBN: 978-3-319-67675-3

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